SOLUTION: Please simplify. 4/the square root of 2-the square root of 6

Algebra ->  Trigonometry-basics -> SOLUTION: Please simplify. 4/the square root of 2-the square root of 6       Log On


   

Question 94463: Please simplify.
4/the square root of 2-the square root of 6
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Please simplify.
4/the square root of 2-the square root of 6
:
4%2F%28%28sqrt%282%29+-+sqrt%286%29%29%29
:
Multiply by the conjugate of the denominator over itself:
4%2F%28%28sqrt%282%29+-+sqrt%286%29%29%29 * %28%28sqrt%282%29+%2B+sqrt%286%29%29%29%2F%28%28sqrt%282%29+%2B+sqrt%286%29%29%29 =
FOIL the denominators, the middle terms cancel
= %28%284sqrt%282%29+%2B+4sqrt%286%29%29%29%2F%28%282+-+6%29%29 = %28%284sqrt%282%29+%2B+4sqrt%286%29%29%29%2F%28-4%29 = %28-sqrt%282%29+-+sqrt%286%29%29
Note the -4 cancels and changes the signs